Illuminating nonlinear dependence of film deposition rate in a CVD reactor on operating conditions

Abstract

Mixed convection flow multiplicities commonly arise in CVD processes, due to the competition between free (natural) and forced convection. The instabilities and the associated solution multiplicity are due to nonlinear terms appearing in the transport equations. The stability interchange between stable and unstable steady states is marked by a pair of turning points on solution branches in parameter space; along them, two stable steady state branches are connected with an unstable one. The case study chosen is that of silicon deposition on a single wafer. To examine the phenomena inside the CVD reactor, the set of coupled transport equations along with a chemistry model for silicon deposition are solved with the commercial code Ansys/Fluent. In contrast to previous works that studied chemistry-free systems, here the effects of nonlinearities are investigated while accounting for the interplay of reaction and transport. Parameter continuation is made possible by the arc-length/RPM algorithm. The film deposition rate on the wafer is computed in every part of the solution branch at different temperature values, which are selected from the various deposition regimes of the Arrhenius plot, namely the diffusion or transport limited, the reaction limited and the transition regimes. Our results reveal multiple Arrhenius plots. In the reaction limited regime, the deposition rate variation along the wafer is similar in both dominant physical mechanisms. However, in the diffusion limited regime, the variations are different; in particular, when forced convection dominates, a significant increase of the deposition rate in the center of the wafer is observed.